Year: 2010
Type: article
Abstract: The dynamical evolution of a recently introduced one-dimensional model [S. Biswas and P. Sen, Phys. Rev. E 80, 027101 (2009)] (henceforth, referred to as model I), has been made stochastic by introducing a parameter $\ensuremath{\beta}$ such that $\ensuremath{\beta}=0$ corresponds to the Ising model and $\ensuremath{\beta}\ensuremath{\rightarrow}\ensuremath{\infty}$ to the original model I. The equilibrium behavior for any value of $\ensuremath{\beta}$ is identical: a homogeneous state. We argue, from the behavior of the dynamical exponent $z$, that for any $\ensuremath{\beta}\ensuremath{\ne}0$, the system belongs to the dynamical class of model I indicating a dynamic phase transition at $\ensuremath{\beta}=0$. On the other hand, the persistence probabilities in a system of $L$ spins saturate at a value ${P}_{sat}(\ensuremath{\beta},L)={(\ensuremath{\beta}/L)}^{\ensuremath{\alpha}}f(\ensuremath{\beta})$, where $\ensuremath{\alpha}$ remains constant for all $\ensuremath{\beta}\ensuremath{\ne}0$ supporting the existence of the dynamic phase transition at $\ensuremath{\beta}=0$. The scaling function $f(\ensuremath{\beta})$ shows a crossover behavior with $f(\ensuremath{\beta})=\text{constant}$ for $\ensuremath{\beta}⪡1$ and $f(\ensuremath{\beta})\ensuremath{\propto}{\ensuremath{\beta}}^{\ensuremath{-}\ensuremath{\alpha}}$ for $\ensuremath{\beta}⪢1$.
Source: Physical Review E
Author: Parongama Sen
Institution: University of Calcutta
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2018649635